Geodesic
An ergodic theorem for regenerating processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 402-405 
G. P. Klimov. An ergodic theorem for regenerating processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 402-405. http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a17/
@article{TVP_1976_21_2_a17,
     author = {G. P. Klimov},
     title = {An ergodic theorem for regenerating processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {402--405},
     year = {1976},
     volume = {21},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a17/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\xi(t)$, $t\ge 0$, be a regenerating process; $B$ be a measurable set in the phase space; $x(t)$ be the indicator of the event $\{\xi(t)\in B\}$. In this paper, a theorem is proved on convergence of $\displaystyle\frac{1}{T}\int_0^T x(t)\,dt$ to a final probability of the event $\{\xi(t)\in B\}$ as $T\to\infty$.